Buoyancy-driven motion of bubbles in square channels

The motion of air bubbles in square capillaries moving under the influence of gravity is studied over a range of Reynolds numbers. The steady shapes and velocities of the bubbles as a function of the bubble size are determined experimentally at moderate Bond and capillary numbers. Bubbles are nearly spherical at lower bubble volumes and become prolate losing their fore and aft symmetry at larger bubble volumes. At higher Weber numbers, a reentrant cavity develops at the rear of bubble. The critical Weber number at which this shape transition occurs lies between 0.89 and 1.38. At small Weber numbers, the terminal velocity of bubbles increases monotonically with bubble volume and eventually reaches a plateau value, which is independent of the bubble size. At higher Weber numbers, a maxima develops in the velocity-volume curve at moderate bubble sizes which grows in magnitude as the Weber number increases. Even at small bubble volumes with nearly spherical shape, the terminal velocity of the bubbles is less than the Hadamard-Rybczynski velocity due to the wall drag. The speed and the maximum bubble width for air bubbles rising in a square channel is higher than that of an air bubble rising in a circular channel with the same hydraulic diameter. The experimental data compares well with predicted trends in the viscous and inertial limits for long bubbles.